/**
 * 64. 最小路径和
 * https://leetcode-cn.com/problems/minimum-path-sum/
 */
public class Solutions_64 {
    public static void main(String[] args) {
        int[][] grid = {{1, 3, 1},
                        {1, 5, 1},
                        {4, 2, 1}};  // output: 7 (1 + 3 + 1 + 1 + 1)

        int result = minPathSum(grid);
        System.out.println(result);
    }

    public static int minPathSum(int[][] grid) {
        int row = grid.length, col = grid[0].length;
        int[][] dp = new int[row][col];

        // dp 第一行设初始值
        for (int i = 0; i < col; i++) {
            dp[0][i] = grid[0][i];
            if (i > 0) {
                dp[0][i] += dp[0][i - 1];
            }
        }
        // dp 第一列设初始值
        for (int i = 0; i < row; i++) {
            dp[i][0] = grid[i][0];
            if (i > 0) {
                dp[i][0] += dp[i - 1][0];
            }
        }
        for (int i = 1; i < row; i++) {
            for (int j = 1; j < col; j++) {
                // 左边与上边的最小值，加上当前坐标上的值
                dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
            }
        }
        // 最右下角的值
        return dp[row - 1][col - 1];
    }
}
